Investigation of electromagnetic wave diffraction from an inhomogeneous partially shielded solid

Diffraction of electromagnetic wave from a partially shielded inhomogeneous dielectric is considered. The original boundary value problem for Maxwell’s equations is shown to have at most one quasi-classical solution. The problem is reduced to a system of integro-differential equations on the solid and the screens. The matrix integro-differential operator is treated in Sobolev spaces and is shown to be a continuously invertible operator. As a result, convergence of the Galerkin method is proved in the chosen functional spaces.